Education Technology

VIC: Pythagoras is not Real

by Texas Instruments


  • Square imaginary numbers (rectangular form)
  • Work with real and imaginary components
  • Informal exploration of Polar form


  • Argand Plane
  • Real component
  • Imaginary component
  • Magnitude / Modulus
  • Angle / Argument

About the Lesson

Students manipulate z plotted on the Argand plane, the corresponding value of z squared is plotted on an adjacent Argand plane. If the real and imaginary components of z are integer quantities then the real and imaginary components of z squared form the shorter side lengths of a Pythagorean triple. After identifying a collection of triples, students are required to prove that this will always work.

An extension activity allows students to also informally explore the polar form of a complex number.